Multiple-Input Multiple-Output (“MIMO”) communication systems are becoming increasingly popular as a solution to increasing demands for higher data-rates and more reliable wireless communication systems. These systems comprise multiple antennas at a transmitter side of the communication system and multiple antennas at the receiver side of the communication system. Each transmitter antenna can transmit a different signal at a common frequency through a different channel of the communication system. Each receiver antenna may receive each signal from the multiple transmitter-antennas. During transit, the transmitted signals may encounter different obstacles such that the frequency response of each channel is different. The plurality of channels used in the transmission of symbols from the plurality of transmitter antennas to the plurality of receiver antennas together form a channel matrix. The input-output relationship of a typical MIMO system can be represented by Equation 1.y=Hs+w  Equation 1:
In Equation 1, y represents an M×1 output vector received by the receiver antennas, s represents an N×1 input symbol vector transmitted by the transmitter antennas, H represents an M×N channel matrix, and w represents an unknown noise vector.
A common goal of conventional systems is to attempt to efficiently detect the transmitted symbol vector s by determining frequency response of each channel in the communication system, i.e. accurately estimating the channel matrix H.
It can be assumed that the elements of noise vector w are independently distributed with each entry of the noise vector being a random variable with zero mean and variance σω2. Given the known distribution of the noise vector, the optimal solution to the MIMO symbol detection problem is Maximum Likelihood (“ML”) detection. ML detection, however, requires an exhaustive search over all possible transmitted symbol vectors, requiring high computational complexity. This approach is infeasible for hardware implementations when either a large signal constellation or a large number of transmit and receive antennas are employed. Hence, a goal of conventional systems is to design hardware for MIMO symbol detection that achieves comparable Bit-Error-Rate (“BER”) performance to the ML detector while having low hardware complexity and meeting throughput and latency requirements, especially as the size of the MIMO system increases.
Some conventional MIMO symbol detections systems employ methods of linear detection and Successive Interference Cancelation (“SIC”). Because most of the required processing for these detectors need only occur at the maximum packet-rate (preprocessing) and the required symbol-rate processing has relatively low-complexity, the throughput requirements for certain wireless standards, such as 802.11n, can be achieved in these systems. These conventional systems, however, do not collect the same diversity (negative logarithmic asymptotic slope of the BER versus Signal-to-Noise-Ratio (“SNR”) curve) as ML detection. As a result, these methods exhibit greatly reduced system performance compared to ML detectors
Other conventional symbol detection systems employ Sphere Decoding (“SD”) algorithms. Hardware implementations of SD algorithms can achieve ML or near-ML performance. Unfortunately, these methods exhibit greatly increased symbol-rate processing complexity compared to linear or SIC detectors. The complexity of SD methods can also vary widely with changing channel conditions.
The maximum packet-rate of 802.11n is considerably less than the symbol-rate. Therefore, it is desirable to obtain detection systems and methods that achieve ML or near-ML performance at the cost of increased preprocessing complexity as opposed to increased symbol-rate processing complexity. Systems having these desired characteristics include Lattice Reduction (“LR”) aided detectors, which, unlike SD methods, incorporate LR algorithms into the preprocessing part of linear or SIC detectors and increase the symbol-rate processing complexity slightly. Specifically, LR systems and methods employ lattice reduction once per received packet (per subcarrier). LR-aided detectors also exhibit the desirable property of having a complexity that is independent of both the channel SNR and signal constellation (assuming individual arithmetic operations have O(1) complexity).
A variety of hardware realizations of LR-aided detectors have been explored to exploit these properties and to achieve near-ML performance. Various explorations have included a VLSI implementation of a simplified Brun's LR algorithm and a software implementation of Seysen's LR algorithm on a reconfigurable baseband processor. Other conventional LR-aided detectors employ variations the Complex Lenstra-Lenstra-Lovász (“CLLL”) LR algorithm. Unfortunately, the performance of these conventional LR-aided detectors decreases and their complexity increases as the size of the MIMO system increases, i.e. the number of transmitter and receiver antennas increases.
Accordingly, there is a desire for more efficient and less complex LR-aided detection systems and methods. Various embodiments of the present invention address these desires.